Reduced Intensity Haploidentical Transplantation for the Treatment of Primary or Secondary Myelofibrosis

OUTLINE: Cohort 1 is now closed and all patients will be enrolled on Cohort 2. COHORT I: JAK INHIBITOR THERAPY: Patients receive a JAK inhibitor at least 8 weeks prior to the start of hematopoietic cell transplantation (HCT) conditioning through day -4 before transplantation. CONDITIONING: Patients receive melphalan intravenously (IV) over 1 hour on day -5, fludarabine IV over 30-60 minutes on days -5 to -2, and undergo total-body irradiation (TBI) on day -1 or day -1 and day 0. TRANSPLANT: Patients receive peripheral blood stem cell infusion on day 0. GVHD PROPHYLAXIS: Patients then receive cyclophosphamide IV over 3 hours on days 3-4, tacrolimus IV beginning day 5 then orally (PO) for about 6 months, mycophenolate mofetil PO twice daily (BID) or three times daily (TID) beginning day 5 for 6 weeks, and granulocyte colony-stimulating factor (G-CSF) subcutaneously (SC) beginning day 7 until neutrophil recovery is \> 1,500/mm\^3. COHORT II: JAK INHIBITOR THERAPY: Patients receive a JAK inhibitor at least 8 weeks prior to the start of HCT conditioning through day -4 before transplantation. Additionally, patients receive a JAK inhibitor following transplantation beginning day +5 through 9-12 months after transplant. CONDITIONING: Patients receive melphalan IV over 1 hour on day -5, fludarabine IV over 30-60 minutes on days -5 to -2, and undergo TBI on day -1 or day -1 and day 0. TRANSPLANT: Patients receive peripheral blood stem cell infusion on day 0. GVHD PROPHYLAXIS: Patients then receive cyclophosphamide IV over 3 hours on days 3-4, tacrolimus IV beginning day 5 then PO for about 6 months, mycophenolate mofetil PO BID or TID beginning day 5 for 6 weeks, and G-CSF SC beginning day 7 until neutrophil recovery is \> 1,500/mm\^3. All patients undergo magnetic resonance imaging (MRI), computed tomography (CT), bone marrow biopsy and aspiration and blood sample collection throughout the trial. Patients also undergo echocardiography (ECHO) or multigated acquisition scan (MUGA) on the trial. After completion of study treatment, patients are followed up between day 80-100, at 1 year, and then up to 5 years.